Bioware have been about filler combat since forever. I don't remember a game from them that didn't have it. I admit, though, that I never got far in BG2 - but I'd be very surprised if it didn't have it.
There´s a variety of aspects tied to the filler combat "problematic":
1. filler combat as something one feels a game would be better off without, because it serves no other purpose than to artificially extent play time, is tedious, boring, repetitive, etc.
2. filler combat as something as a "legitimate" design practice, aka something that makes the world feel more alive, maintains a sense of contrast, may cut into player´s resources in non-negligible ways in the long run, etc.
3. is it part of the mandatory game´s content, or is it only reserved for optional parts?
4. combat system, which may significantly affect how much time player has to devote to filler combat compared to non-filler and to what degree the presence of filler combat affects the overall game´s pacing
I´m replaying the whole "saga" right now (2/3 of ToB left) and while my perception is certainly skewed due to the mods installed (Sword Coast Stratagems and Ascension being the main culprits), taking the above points into consideration, I´d say neither game is a bad-kind-of-filler-heavy. There is a lot of combat filler, but such encounters are mostly quite justified to be in and are over fast. And when it comes to "mandatory" filler, there´s actually quite little of it (with SCS, more of the filler
is pretty much mandatory because going against, say, Irenicus in Hell would be suicide without sufficient level/resources, but that´s a different matter).
That goes for BG1 + BG2 vanilla only though, they went overboard with combat in Throne of Bhaal.
Regarding linearity, BG2 had a large part of the game where your only goal was to raise money and where you had any number of different quests you could perform in whatever order you wanted. As a result you might be several levels higher when completing quest A then you would be for quest B. This is what I meant by less linear, the fact that there were quests that you had to perform but you could do them in any order and your power level could change dramatatically from one to the next.
And this is different from BG1 how?
The game´s main quest is linear in that there are certain mandatory plot points (chapter transitions) which you need to go through in a given order, but you´re given quite a leeway in what to do in-between or how to reach these points.
There´s a big amount of maps you can explore before even touching the main quest (and end up going against the Nashkel kobolds with a level 7 party, for example), or you can explore these in chunks along the main quest, once you´re in Baldur´s Gate you can skip some of the seemingly mandatory content by exploring the Iron Throne building right away (you don´t even have to fight the party at the uppermost level, iirc), etc.
Just about the only general difference between both games is the one branching occurrence in BG2, but otherwise both games maintain similar degree and type of (non)linearity and to me BG1 actually feels overall less linear than BG2.
At any rate, linear main quest doesn´t necessarily mean linear game.
As a sidenote, both games are also kinda similar in that they have, in my opinion, issues with balancing/placing the optional bits - in BG1 it´s pretty much impossible to go through the expansion parts at appropriate time as it either skews balance in the main game or doesn´t make much sense from a story perspective, and in BG2 the sense of urgency goes strongly against completionist-y approach in general (can be quite elegantly "fixed" by raising the sum needed for ship to 60000 or so).
My whole point is that was why I was so impresed with the battles in DA:O, even the filler combats could still be fun and challenging and you could still lose.
But if one finds a lot of these fights repetitive, the fact they´re challenging and time consuming to boot is very likely detrimental to the one´s overall enjoyment. Due to its combat system and encounter/enemy design, in BG2 you can breeze through the filler fast, which means the filler isn´t memorable and it´s easier to remember the game for its mage duels and boss fights, whereas in the case of DA:O, the fact one may spend proportionately quite a lot of time in encounters which one doesn´t find outstanding in any way may be a problem.
Personally I didn´t quite mind the usual suspect, Deep Roads, because I liked the atmosphere there and I´ve found the latter half well put together, but Carta hideout or the cultist temple really got on my nerves in this regard more than anything in BG2, at least if I exclude Throne of Bhaal.